复合材料层合夹芯板局部变形行为研究

在局部荷载作用下,带软夹芯层的夹芯板结构将产生一定的局部变形现象。本文采用双参数基础模型模拟软夹芯材料与受载层合面板间的相互作用,基于经典层合板理论,推导并给出了夹芯板结构局部变形问题的半解析分析方法,并通过算例讨论了边界条件、荷载作用方式、夹芯层厚度与弹性模量等因素对该类结构局部弯曲和局部屈曲行为的影响。     

On the Response of a Sandwich Panel with a Bilinear Core

Sandwich panels can failin a variety of ways. In the present article one type of failure is investigated and modeled that has a number of important applications, e.g., marine hulls. Here core yielding is assumed to initiate and grow in the sandwich panel while the face sheets remain bonded, unbuckled, and in the elastic range. For elastic face sheets, the core shear stresses can be determined from equilibrium of the face sheets independent of core yield. Core shear strains can then be found from the stress-strain curve and an algorithm is constructed for determining shear deflection. Bending deflection is found from the elastic solution. This approach works well except when the bilinear stress-strain behavior approaches the perfectly plastic core. With the aid of a detailed finite-element solution, it is shown that the classical sandwich theory assumptions begin to break down and that the face sheets now carry an appreciable part of the shear load. This effect is shown in detail for four-point beam bending, for which the classical sandwich solution is 20-30% below the ABAQUS results and the experimental data. For the bilinear case, not close to perfectly plastic, however, the extension of the classical theory to the coreyielding problem provides excellent results.     

A simple finite element for beams on elastic foundations

A simple "routine" beam on elastic foundation finite element using a polynomial displacement function has been developed which yields acceptably accurate deflection, shear and bending moment values for prismatic or non-prismatic beams of elastic material resting on foundations with varying or nonlinear subgrade reactions. Limited extension of the formulation to an "exact" finite element using the exact displacement function of a beam on elastic foundation has also been carried out. The subgrade is represented by a non-homogeneous solid medium to include nonlinear parameters if required. The iterative solution is extended to cases where the beam may uplift because the foundation is a no tension material. The model is also suitable for calculating the elastic deflections, membrane. and bending stress resultants for axisymmetrically loaded variable thickness shells of revolution. A computer program called FEBEF [finite element: beam on elastic foundation] incorporating the routine finite element has been prepared for the solution of beams on elastic foundations and axi symmetrically loaded shells of revolution.     

Bending of Circular Sandwich Plate on Elastic Foundation

Bending of elastic circular sandwich plate with light filler, which is on an elastic foundation, is considered. To describe the kinematics of plate bending that is nonsymmetric in sandwich thickness, broken normal hypotheses are accepted. The foundation reaction is described by the Winkler model. The load is local symmetrical. A set of equilibrium equations and their exact solution in displacements have been obtained. Numerical results for a metal-polymeric sandwich plate are given. __________ Translated from Problemy Prochnosti, No. 6, pp. 68 – 78, November – December, 2005.     

Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets

This paper studied the large amplitude vibration and the nonlinear bending of a sandwich plate with carbon nanotube-reinforced composite (CNTRC) face sheets resting on an elastic foundation in thermal environments. The material properties of CNTRC face sheets are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The governing equation of the plate that includes plate-foundation interaction is solved by a two-step perturbation technique. The thermal effects are also included and the material properties of both CNTRC face sheets and homogeneous core layer are assumed to be temperature-dependent. A detailed parametric study is conducted to study the effects of nanotube volume fraction, core-to-face sheet thickness ratio, temperature change, foundation stiffness and in-plane boundary conditions on the nonlinear vibration characteristics and nonlinear bending behaviors of sandwich plates with functionally graded CNTRC face sheets. The results for the same plate with uniformly distributed CNTRC face sheets are also provided for comparison.     

Delamination of layered structures on elastic foundation

This study presents an interface fracture mechanics analysis of delamination of a layered beam resting on a Winkler elastic foundation subject to general mechanical loads. A crack tip element on elastic foundation model is established first, through which, two concentrated forces existing at the crack tip are determined in closed-form. Then total energy release rate of the crack can be expressed in term of these two forces. By using available numerical results in the literature, the phase angle of the total energy release rate is also obtained. To verify the validity and accuracy of the solutions, debonding of a bonded overlay from the base structure resting on a Winkler elastic foundation is analyzed using the present solution. Comparisons with the baseline results obtained by finite element analysis suggest that the present analytical solution provides an excellent estimation of the total energy release rate and its phase angle for interface cracks in layered structure on elastic foundation. This study provides an approximated analysis of the debonding of a thin overlay debonding from the concrete pavement, where the effect of the base structure is simplified by a Winkler elastic foundation. This solution can also be used to analyze other similar delamination problems, such as local delamination in laminated composites, and face sheet delimitation in sandwich beams.     

弹性基础上夹层圆板大挠度问题的精确解

到目前为止,弹性基础上夹层板大挠度问题的研究尚未见报道。本文用幂级数求解,碍到了弹性基础上轴对称夹层圆板大挠度问题的精确解,并进行了大量数值计算,列出了有关图表,可供工程设计参考。     

Stress analysis of axially and thermally loaded discontinuous tile core sandwich with and without adhesive filled core gaps

An analytical study is performed to investigate the stress states in an axially and thermally loaded sandwich structure with a discontinuous ceramic tile core. General and simplified models are developed to determine stresses in the constituents of the sandwich structure with and without adhesive in the gaps between adjacent tiles. A general model that allows local bending of the face sheet and a simplified model which assumes uniform through-thickness stress distribution in the face sheets are developed. It is shown that the normal stress in the face sheet decreases when the gap is filled by adhesive, although the tile stress increases. The analytical model shows that normal and shear stresses at the face/core interface can be reduced by filling the gaps between tiles. Filled gaps also elevate the axial stiffness of the structure. Model results are verified by comparison to a previously developed analytical model and finite element analysis.     

Bending response of web-core sandwich beams

This paper presents a new analytical solution for the bending response of a web-core sandwich beam. The beam is a transverse cut from the sandwich plate. The method is based on the plane frame analysis, where the response of the beam is divided into local and global components. The Clebsch’s method is used to calculate the deflection of the face plates. The validation of the plane frame method is carried out with FE-analyses based on the shell element formulation. Also a comparison is made with the method based on homogenized beam. Periodic stress distributions in the face plates are revealed with the plane frame analysis and are supported by the FE-analysis. The existing methods based on homogenized beam are not able to predict these stresses. The plane frame analysis can benefit the development of the theory related to web-core sandwich plate.     

Nonlinear analysis of sandwich plates with FGM face sheets resting on elastic foundations

Nonlinear vibration, nonlinear bending and postbuckling analyses are presented for a sandwich plate with FGM face sheets resting on an elastic foundation in thermal environments. The material properties of FGM face sheets are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equation of the plate that includes plate-foundation interaction is solved by a two-step perturbation technique. The thermal effects are also included and the material properties of both FGM face sheets and homogeneous core layer are assumed to be temperature-dependent. The numerical results reveal that the foundation stiffness and temperature rise have a significant effect on the natural frequency, buckling load, postbuckling and nonlinear bending behaviors of sandwich plates. The results also reveal that the core-to-face sheet thickness ratio and the volume fraction distribution of FGM face sheets have a significant effect on the natural frequency, buckling load and postbuckling behavior of the sandwich plate, whereas this effect is less pronounced for the nonlinear bending, and is marginal for the nonlinear to linear frequency ratios of the same sandwich plate.     

Bending analysis of FG viscoelastic sandwich beams with elastic cores resting on Pasternak’s elastic foundations

The investigation of bending response of a simply supported functionally graded (FG) viscoelastic sandwich beam with elastic core resting on Pasternak’s elastic foundations is presented. The faces of the sandwich beam are made of FG viscoelastic material while the core is still elastic. Material properties are graded from the elastic interfaces through the viscoelastic faces of the beam. The elastic parameters of the faces are considered to be varying according to a power-law distribution in terms of the volume fraction of the constituent. The interaction between the beam and the foundations is included in the formulation. Numerical results for deflections and stresses obtained using the refined sinusoidal shear deformation beam theory are compared with those obtained using the simple sinusoidal shear deformation beam theory, higher- and first-order shear deformation beam theories. The effects due to material distribution, span-to-thickness ratio, foundation stiffness and time parameter on the deflection and stresses are investigated.     

Tailoring Sandwich Face/Core Interfaces for Improved Damage Tolerance—Part II: Experiments

Various modifications of the face/core interface in foam core sandwich specimens are examined in a series of two papers. This paper constitutes part I and describes the finite element analysis of a sandwich test specimen, i.e. a DCB specimen loaded by uneven bending moments (DCB-UBM). Using this test almost any mode-mixity between pure mode I and mode II can be obtained. A cohesive zone model of the mixed mode fracture process involving large-scale bridging is developed. Results from the analysis are used in Part II, which describes methods and results of a series of experiments.     

Tailoring Sandwich Face/Core Interfaces for Improved Damage Tolerance—Part I: Finite Element Analysis

Various modifications of the face/core interface in foam core sandwich specimens are examined in a series of two papers. This paper constitutes part I and describes the finite element analysis of a sandwich test specimen, i.e. a DCB specimen loaded by uneven bending moments (DCB-UBM). Using this test almost any mode-mixity between pure mode I and mode II can be obtained. A cohesive zone model of the mixed mode fracture process involving large-scale bridging is developed. Results from the analysis are used in Part II, which describes methods and results of a series of experiments.     

Local effects in the vicinity of inserts in sandwich panels

The paper considers local bending effects induced in the vicinity of inserts in sandwich panels. Such local bending effects are associated with an increase of bending stresses in the sandwich faces and normal and shear stresses in the sandwich core. An earlier developed analytic model [Proceedings of the Sixth International Conference on Sandwich Structures (ICSS-6) (2002) 551] is adapted for the case of a sandwich panel with circular insert, with elastic properties differing from those of the core. The locally induced stresses in the faces and core due to presence of the insert are expressed via simple analytic relations (and charts) enabling an estimation of these local stresses. Finite element analysis is employed to demonstrate the applicability of the analytic model, and a good correspondence between the numerical and the analytical data is found. A study case related to marine applications, namely a circular insert in a sandwich deck panel used for mounting of a rigging fixture, is considered, and optimization of an existing design is carried out.     

The structural response of clamped sandwich beams subjected to impact loading

The structural response of dynamically loaded monolithic and sandwich beams made of aluminum skins with different cores is determined by loading the end-clamped beams at mid-span with metal foam projectiles. The sandwich beams comprise aluminum honeycomb cores and closed-cell aluminum foam cores. Laser displacement transducer was used to measure the permanent transverse deflection of the back face mid-point of the beams. The resistance to shock loading is evaluated by the permanent deflection at the mid-span of the beams for a fixed magnitude of applied impulse and mass of beam. It is found that sandwich beams with two kind cores under impact loading can fail in different modes. Experimental results show the sandwich beams with aluminum honeycomb cores present mainly large global deformation, while the foam core sandwich beams tend to local deformation and failure, but all the sandwich beams had a higher shock resistance, then the monolithic beam. For each type of beams, the dependence of transverse deflection upon the magnitude of the applied impulse is measured. Moreover, the effects of face thickness and core thickness on the failure and deformation modes were discussed. Results indicated that the structural response of sandwich beams is sensitive to applied impulse and structural configuration. The experimental results are of worth to optimum design of cellular metallic sandwich structures.     

分布载荷作用下简支功能梯度夹层板的弯曲分析

研究了四边简支具有功能梯度芯材的夹层板在分布载荷作用下的弯曲问题。基于Reissner假设, 根据功能梯度材料的本构方程得出了应力、位移及内力的表达式, 得到功能梯度夹层板的平衡方程; 针对四边简支的边界条件, 通过将挠度 w 与横向剪力 Q_x、Q_y 用双三角级数展开的方法, 求解平衡方程。采用本文方法分别求解了均布载荷作用下、芯材弹性模量线性变化的功能梯度夹层板与芯材为均质各向同性材料的夹层板的弯曲挠度, 并通过与经典解及有限元解进行比较, 证明了本文方法的正确性。     

夹层输流管道弹性波频散特征分析

对无限长夹层输流管道的管壁弹性波频散特征、管内流体声波频散特征,以及弹性体与流体声固耦合的波传播频散特征进行了研究与分析.基于铁木辛柯梁模型构建弹性体管道的波数解析式.考虑声固耦合效应,对无限长夹层输流管道的管壁弹性波与管内流体声波相互耦合的波数和模态振型进行了求解.运用参数化扫描,分别计算了管内流体域为水和空气情况下...     

Bending and vibration of CFRP-faced rectangular sandwich plates

A linear analysis is presented for bending and vibration of sandwich plates consisting of an orthotropic core and unbalanced laminated face plates. A solution method is proposed through the principle of minimum total potential energy, and a double Fourier series approach is used for the displacement functions. Analytical and experimental investigations are performed for fully clamped boundary conditions, and the results show reasonable correlation. Holographic techniques were used to obtain the deflection and vibration modes.     

Local effects across core junctions in sandwich panels

Sandwich beams and panels with symmetric faces and cores of varying stiffness are investigated. The paper presents a theoretical and experimental study of the local effects that occur in the vicinity of intersections between cores of different stiffness in such sandwich panels. These local effects manifest themselves by a significant rise of the bending stresses in the faces in the vicinity of the core junctions. Closed-form estimates of the stress/strain fields induced by local effects are presented for sandwich beams and panels loaded in cylindrical bending. The accuracy of the derived closed-form estimates is verified experimentally for the case of a sandwich beam in three-point bending.     

Intensity of Local Effects at the Core Junctions in Sandwich Panels

Local effects that occur in the vicinity of junctions between different cores in sandwich panels subjected to the in-plane axial force and bending moment are considered. These local effects manifest themselves in a rise of locally induced bending normal stresses in the sandwich faces and shear and normal stresses in the cores in the near vicinity of the core junctions. Intensity of the local effects is measured experimentally for a representative sandwich beam subjected to both types of loadings. The numerical simulations are performed using Finite Element Analysis, and they reveal significant rates of stress concentrations in the faces and cores adjacent to the core junctions. The intensity of the local effects is dependable on the geometry and elastic properties of the sandwich faces and a degree of dissimilarity of elastic properties of the adjoined cores.